In the computer art, it is desirable in many instances, to employ the use of systems that have both digital and analog capabilities. Such systems are known as hybrid computers and permit the user to introduce both analog data, represented by indiscrete amplitude of electrical signals, and digital data represented by a coded sequence order of signals having only discrete states. In response to these two types of signal data, the hybrid computer performs analog and digital operations and integrates the separate operations by means of analog to digital or digital to analog converters. The advantage of the hybrid is the ability to solve problems wherein the input data are partially compatable with each of the analog and digital operations. Furthermore, it permits the generation of a visual representation of the output function.
One of the most important applications of hybrid is their ability to solve problems involving undefinable or difficult to define relationships. Therefore, it is useful to incorporate into hybrid systems, function generators that are capable of producing analog output functions in response to an independently varying analog input signal.
A prime example of the use of hybrids is in the aerospace industry in which aerodynamic characteristics of missile and airplane systems are determined by wind tunnel tests. It is often necessary to simulate these relationships in an analog computer. For example, angle of attack and mach number are independent variables that must be simulated in the hybrid to produce a continuous function that airframe designers can study to determine the effect of the parameters on a given system.
Any arbitrary mathematical function of one variable F(x) can be represented to any degree of accuracy by a set of straight line segments F(x) = a + bx. This implies that each F.sub.i (x) can be represented as a.sub.i + b.sub.i x where a.sub.i and b.sub.i are the intercept and slope of the ith straight line segment. The function a + bx is easily implemented in hardware by the use of hybrid function generators composed of, such as a multiplying digital to analog converter (mdac), a digital analog converter (dac), and a summer. The function of the mdac is to multiply the continuous analog input x by the digital value b.sub.i to form the continuous signal bx. The signal bx is then summed with the output of the dac to form a + bx. The mathematical derivation to extend this concept to functions of two variables is as follows: ##STR1## To get F(x,y) a linear interpolation between F(x.sub.i, y) and F(x.sub.i+1, y) is performed resulting in ##STR2## Carrying out the algebraic manipulations involved EQU F(x,y) = K.sub.1 (a + bx) + K.sub.2 [(c + dx)y] 4)
Where
a, b, c, and d are functions of x.sub.i, x.sub.i.sub.+1, y.sub.j and y.sub.j.sub.+1 PA1 K.sub.1 and K.sub.2 are scaling constants.
and
Therefore if x and y lie in the ijth sector of the xy grid EQU F.sub.ij (x,y) = K.sub.1 (a.sub.ij + b.sub.ij x) + K.sub.2 [(c.sub.ij + d.sub.ij x)y]. 5)
It should be observed that F.sub.ij is not a plain surface but rather a hyperboloid since it is constrained to pass through 4 points.
The prior art has been deficient in providing a hybrid system for producing an output that is a function of two independent variables, that is simple to use and efficiently processes the input data.